cutcutcodec.core.signal.window.alpha_to_band

cutcutcodec.core.signal.window.alpha_to_band(alpha: float) → float

Empirical estimation based on regression.

The fitted model is \(band = a*\alpha + b + c*tanh(d*\alpha)\).

This function is close to the identity function.

Examples

>>> import torch
>>> from cutcutcodec.core.signal.window import find_dpss_law
>>> alphas, _, bands = find_dpss_law()
>>> alphas, bands = alphas.to(torch.float64), bands.to(torch.float64)
>>> abcd = torch.tensor([0.932, 0.815, -0.559, 1.61], dtype=torch.float64, requires_grad=True)
>>> optim = torch.optim.Adam([abcd])
>>> for _ in range(10000):
...     pred = abcd[0]*alphas + abcd[1] + abcd[2]*torch.tanh(abcd[3]*alphas)
...     optim.zero_grad()
...     torch.mean((bands - pred)**2).backward()
...     optim.step()
...
>>> abcd.detach().to(torch.float32)
tensor([ 0.9321,  0.8148, -0.5588,  1.6099])
>>> # import matplotlib.pyplot as plt
>>> # _ = plt.plot(alphas.numpy(force=True), bands.numpy(force=True))
>>> # _ = plt.plot(alphas.numpy(force=True), pred.numpy(force=True))
>>> # plt.show()
>>>